Given $ m \angle AOB = 8x - 105$, and $ m \angle BOC = 9x - 38$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {8x - 105} + {9x - 38} = {180}$ Combine like terms: $ 17x - 143 = 180$ Add $143$ to both sides: $ 17x = 323$ Divide both sides by $17$ to find $x$ $ x = 19$ Substitute $19$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 8({19}) - 105$ Simplify: $ {m\angle AOB = 152 - 105}$ So ${m\angle AOB = 47}$.